In this paper, we first prove that if the edges of K2m are properly colored by 2m - 1 colors in such a way that any two colors induce a 2-factor of which each component is a 4-cycle, then k2m can be decomposed into m isomorphic multicolored spanning trees. Consequently, we show that there exist three disjoint isomorphic multicolored spanning trees in any properly (2m-l)-edge-colored K2m for m ≥ 14.
|Number of pages||8|
|State||Published - 1 Jan 2015|
- Complete graph
- Multicolored spanning trees